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Boundedness in a haptotactic model of cancer interactions with fusogenic oncolytic virus. (English) Zbl 07896649

Summary: This paper investigates a haptotactic cross-diffusion model \[ \begin{cases} c_t = D_c \Delta c - \eta_c \nabla \cdot (c \nabla u) + \mu_1 c - \mu_1c^\gamma - \rho c v - \kappa c i, \\ i_t = D_i \Delta i - \eta_i \nabla \cdot (i \nabla u) + \rho c v + p_0 \kappa c i - \delta_i i, \\ s_t = D_s \Delta s - \eta_s \nabla \cdot (s \nabla u) + \left(1-p_0\right) \kappa c i - \delta_s s, \\ u_t = -u \left(\alpha_c c + \alpha_i i + \alpha_s s \right) + \mu_2 u(1-u), \\ v_t = D_v \Delta v - \eta_v \nabla \cdot(v \nabla u) + b_i i + b_s s - \rho c v - \delta_v v \end{cases} \] in a bounded domain \(\Omega \subset \mathbb{R}^2\) with smooth boundary. The model highlights the impact of syncytia formation triggered by fusogenic oncolytic virus on therapeutic efficacy, in addition to the influence of the extracellular matrix (ECM) taxis over the tumor-oncolytic virus interactions. It is proved that under appropriate structural assumptions on the system parameters and sufficiently smooth initial data, the model possesses one global bounded solution.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
35K59 Quasilinear parabolic equations
35K65 Degenerate parabolic equations
82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
Full Text: DOI

References:

[1] Multiscale modelling of cancer response to oncolytic viral therapy, Math. Biosci., 310, 76-95, 2019 · Zbl 1425.92103 · doi:10.1016/j.mbs.2018.12.018
[2] T. Alzahrani, R. Eftimie and D. Trucu, Multiscale moving boundary modelling of cancer interactions with a fusogenic oncolytic virus: the impact of syncytia dynamics, Math. Biosci., 323 (2020), 22 pp. · Zbl 1437.92056
[3] Fusogenic viruses in oncolytic immunotherapy, Cancers, 10, 216, 2018
[4] Viral oncolysis by herpes simplex virus and other viruses, Cancer Biol. Ther., 4, 524-531, 2005
[5] Boundedness in a haptotactic cross-diffusion system modeling oncolytic virotherapy, J. Differ. Equ., 270, 94-113, 2021 · Zbl 1452.35077 · doi:10.1016/j.jde.2020.07.032
[6] Boundedness in a chemotaxis-haptotaxis model with nonlinear diffusion, Nonlinearity, 29, 1564-1595, 2016 · Zbl 1338.35438 · doi:10.1088/0951-7715/29/5/1564
[7] Global boundedness of solutions to a chemotaxis-haptotaxis model with tissue remodeling, Math. Models Methods Appl. Sci., 28, 2211-2235, 2018 · Zbl 1416.35052 · doi:10.1142/S0218202518400134
[8] Global classical solvability in a three-dimensional haptotaxis system modeling oncolytic virotherapy, Math. Methods Appl. Sci., 44, 9275-9291, 2021 · Zbl 1475.35363 · doi:10.1002/mma.7354
[9] G. Ren and J. Wei, Analysis of a two-dimensional triply haptotactic model with a fusogenic oncolytic virus and syncytia, Z. Angew. Math. Phys., 72 (2021), 23 pp. · Zbl 1466.35241
[10] Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion, SIAM J. Math. Anal., 46, 1969-2007, 2014 · Zbl 1301.35189 · doi:10.1137/13094058X
[11] Dampening effects on global boundedness and asymptotic behavior in an oncolytic virotherapy model, J. Differ. Equ., 308, 57-76, 2022 · Zbl 1479.35119 · doi:10.1016/j.jde.2021.11.003
[12] Energy-type estimates and global solvability in a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant, J. Differ. Equ., 257, 784-815, 2014 · Zbl 1295.35144 · doi:10.1016/j.jde.2014.04.014
[13] Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy, J. Differ. Equ., 268, 4973-4997, 2020 · Zbl 1430.35132 · doi:10.1016/j.jde.2019.10.046
[14] Asymptotic behavior of a three-dimensional haptotactic cross-diffusion system modeling oncolytic virotherapy, Math. Models Methods Appl. Sci., 33, 2313-2335, 2023 · Zbl 1530.35126 · doi:10.1142/S0218202523400043
[15] Q. Wen and B. Liu, Global boundedness in an oncolytic virotherapy model with generalized logistic source, Z. Angew. Math. Phys., 74 (2023), 33 pp. · Zbl 1506.35027
[16] Q. Zhao and B. Liu, Dampening effects on global boundedness in a quartic haptotactic model with fusogenic oncolytic virus and syncytia, Z. Angew. Math. Phys., 73 (2022), 21 pp. · Zbl 1502.35186
[17] Global classical solutions to a higher-dimensional doubly haptotactic cross-diffusion system modeling oncolytic virotherapy, J. Differ. Equ., 340, 111-150, 2022 · Zbl 1500.35067 · doi:10.1016/j.jde.2022.08.032
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